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Efficient Interactive Methods for a Class of Multiattribute Shortest Path Problems

Author

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  • Mordechai I. Henig

    (Faculty of Management, Tel Aviv University, Tel Aviv, Israel)

Abstract

Given an acyclic network and a preference-order relation on paths, when and how can Bellman's principle of optimality be combined with interactive programming to efficiently locate an optimal path? We show that if preferences are defined via a collection of attributes, then, under common conditions, the principle of optimality is valid if and only if the preferences can be represented by a linear (value) function over the attributes. Consequently, an interactive programming method is suggested which assesses the value function while using the principle of optimality to efficiently search for an optimal path.

Suggested Citation

  • Mordechai I. Henig, 1994. "Efficient Interactive Methods for a Class of Multiattribute Shortest Path Problems," Management Science, INFORMS, vol. 40(7), pages 891-897, July.
    • Handle: RePEc:inm:ormnsc:v:40:y:1994:i:7:p:891-897
    DOI: 10.1287/mnsc.40.7.891
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    Cited by:

    1. Frini, Anissa & Guitouni, Adel & Martel, Jean-Marc, 2012. "A general decomposition approach for multi-criteria decision trees," European Journal of Operational Research, Elsevier, vol. 220(2), pages 452-460.
    2. Gavish, Bezalel, 1997. "Low earth orbit satellite based communication systems -- Research opportunities," European Journal of Operational Research, Elsevier, vol. 99(1), pages 166-179, May.
    3. Goldberg, Noam & Poss, Michael, 2020. "Maximum probabilistic all-or-nothing paths," European Journal of Operational Research, Elsevier, vol. 283(1), pages 279-289.
    4. J. Puerto & F.R. Fernández, 1998. "Pareto‐optimality in classical inventory problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(1), pages 83-98, February.

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